2018/12/20 by Yongju Bae, Bae, Yongju, J. Scott Carter +3
Computer Science · Engineering · Mathematics · #20B99 #57M10 #57M25 #57Q45 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Group Theory (math.GR) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1812.08475
openalex publication_date 2018/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Semi-direct products of finite groups have permutation representations that are constructed from the permutation representations of their constituents. One can envision these in a metaphoric sense in which a rope is made from a bundle of threads. In this way, subgroups and quotients are easily visualized. The general idea is applied to the finite subgroups of the special unitary group of (2× 2)-matrices. Amusing diagrams are developed that describe the unit quaternions, the binary tetrahedral, octahedral, and icosahedral group as well as the dicyclic groups. In all cases, the quotients as subgroups of the permutation group are readily apparent. These permutation representations lead to injective homomorphisms into semi-direct products.